Homework Answers
ME 32200 Programming course (MATLAB) 4. Please finish the following Matlab code for solving the ODE:...
ME 32200 Programming course (MATLAB)
4. Please finish the following Matlab code for solving the ODE: dy = y(1+1) dt I.C. y(0) = 0 with the multi-step 4th order Milne's Method, and apply 4th order Runge Kutta method to the first 4 points (1 boundary point and the next 3 points). (Hint: 4th order Milne's Method Predictor: 7i+ = Y-3 +h(2f;- fi- +25,-2) Corrector: y = y + + +0. +45j + fi-) Where f; = f(t;,y,) and Fit =...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
2. Consider the following first-order ODE from x = 0 to x = 2.4 with y(0)...
2. Consider the following first-order ODE from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler's explicit method using h=0.6 (b) solving with midpoint method using h= 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).
Solve the following ode using Laplace transform: y' - 5y = f(t); y(0) - 1 t;...
Solve the following ode using Laplace transform: y' - 5y = f(t); y(0) - 1 t; Ost<1 f(t) = 0; t21
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = {...
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...
3. Consider the following ODE: (1 + 2%)/" - xy + y = 0 (a) Find...
3. Consider the following ODE: (1 + 2%)/" - xy + y = 0 (a) Find the first 3 nonzero terms of the power series expansion (around x = 0) for the general solution. (b) Use the ratio test to determine the radius of convergence of the series. What can you say about the radius of convergence without solving the ODE? (c) Determine the solution that satisfies the initial conditions y(0) = 1 and (0) = 0.
Use Euler’s method to approximate the solution of the ODE dx/dt = t − x, x(0)...
Use Euler’s method to approximate the solution of the ODE dx/dt = t − x, x(0) = 1 up to time t = 0.5 with a step size of h = 0.1. Find the actual solution of the equation and graph the approximate solution and the actual solution.
We have this simple ODE model subject to x(0) = x0 ≥ 0, y(0) = y0...
We have this simple ODE model subject to x(0) = x0 ≥ 0, y(0) =
y0 ≥ 0 (you may choose values of x0 and y0). The constants α, β
> 0.
Question: Find an ODE for y(t) by eliminating x. Solve this ODE
analytically. Plot solutions using Mathematica.
x — ау dx dt dy dt = Вх y
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b...
any help on these two questions please??
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b) Find the general real solution of the linear ODE x(t)-Ax(t) + b(t). (c) Solve the initial value problem x(t) = A2(t) + b(t), x(0) = (-2,0,2)T 4.5: Determine the general solution of the ODE x"(t)-x"(t)-r(t) + x(t) = t cost.
4.4: Let 1 0 1 and b(t)- -1 1 0...
x(0)=1, x'O)= 0, where f(t) = 1 if t< 2; and f(t) = 0 if Find...
x(0)=1, x'O)= 0, where f(t) = 1 if t< 2; and f(t) = 0 if Find the solution of X"' + 2x' + x=f(t), t> 2.
ME 32200 Programming course (MATLAB)
4. Please finish the following Matlab code for solving the ODE: dy = y(1+1) dt I.C. y(0) = 0 with the multi-step 4th order Milne's Method, and apply 4th order Runge Kutta method to the first 4 points (1 boundary point and the next 3 points). (Hint: 4th order Milne's Method Predictor: 7i+ = Y-3 +h(2f;- fi- +25,-2) Corrector: y = y + + +0. +45j + fi-) Where f; = f(t;,y,) and Fit =...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
2. Consider the following first-order ODE from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler's explicit method using h=0.6 (b) solving with midpoint method using h= 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).
Solve the following ode using Laplace transform: y' - 5y = f(t); y(0) - 1 t; Ost<1 f(t) = 0; t21
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...
3. Consider the following ODE: (1 + 2%)/" - xy + y = 0 (a) Find the first 3 nonzero terms of the power series expansion (around x = 0) for the general solution. (b) Use the ratio test to determine the radius of convergence of the series. What can you say about the radius of convergence without solving the ODE? (c) Determine the solution that satisfies the initial conditions y(0) = 1 and (0) = 0.
We have this simple ODE model subject to x(0) = x0 ≥ 0, y(0) =
y0 ≥ 0 (you may choose values of x0 and y0). The constants α, β
> 0.
Question: Find an ODE for y(t) by eliminating x. Solve this ODE
analytically. Plot solutions using Mathematica.
x — ау dx dt dy dt = Вх y
any help on these two questions please??
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b) Find the general real solution of the linear ODE x(t)-Ax(t) + b(t). (c) Solve the initial value problem x(t) = A2(t) + b(t), x(0) = (-2,0,2)T 4.5: Determine the general solution of the ODE x"(t)-x"(t)-r(t) + x(t) = t cost.
4.4: Let 1 0 1 and b(t)- -1 1 0...
x(0)=1, x'O)= 0, where f(t) = 1 if t< 2; and f(t) = 0 if Find the solution of X"' + 2x' + x=f(t), t> 2.
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